The structure of the critical set in the mountain-pass theorem for nondifferentiable functions.
type: Item
instance of: scholarly article
title: The structure of the critical set in the mountain-pass theorem for nondifferentiable functions.
zbMATH Open document ID: 1033.49026
author: Giuseppina Barletta
author: Salvatore A. Marano
published in: Differential and Integral Equations
publication date: 2003-11-17T00:00:00Z
review text: The paper studies the structure of the critical set at the level given by the minimax value in the mountain pass theorem for nonsmooth functionals expressed as a sum of a locally Lipschitz function and a proper, convex, lower semicontinuous function on a Banach space. The analysis relies on suitable deformation properties which hold for this class of nonsmooth functionals. One obtains significant information on the nature of the critical points, for instance, establishing the presence of a saddle-point. The authors' theorems extend the classical results due to [\textit{P. Pucci} and \textit{J. Serrin}, ``Extensions of the mountain pass theorem'', J. Funct. Anal. 59, 185--210 (1984; Zbl 0564.58012)]. A special attention is paid in the final part of the paper to the case of purely locally Lipschitz functionals.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2004937
zbMATH Keywords: critical point
zbMATH Keywords: mountain pass theorem
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: deformation
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2004937